DISCUSSION PAPER SERIES No. 4003 UNILINGUAL VERSUS BILINGUAL EDUCATION SYSTEM: A POLITICAL ECONOMY ANALYSIS Javier Ortega ad Thoas P Tageraas LABOUR ECONOMICS ABCD www.cepr.org Available olie at: www.cepr.org/pubs/dps/dp4003.asp www.ssr.co/xxx/xxx/xxx
UNILINGUAL VERSUS BILINGUAL EDUCATION SYSTEM: A POLITICAL ECONOMY ANALYSIS ISSN 0265-8003 Javier Ortega, Uiversité de Toulouse (GREMAQ, IDEI) ad CEPR Thoas P Tageraas, The Research Istitute of Idustrial Ecooics (IUI), Stockhol Discussio Paper No. 4003 August 2003 Cetre for Ecooic Policy Research 90 98 Goswell Rd, Lodo EC1V 7RR, UK Tel: (44 20) 7878 2900, Fax: (44 20) 7878 2999 Eail: cepr@cepr.org, Website: www.cepr.org This Discussio Paper is issued uder the auspices of the Cetre s research prograe i LABOUR ECONOMICS. Ay opiios expressed here are those of the author(s) ad ot those of the Cetre for Ecooic Policy Research. Research disseiated by CEPR ay iclude views o policy, but the Cetre itself takes o istitutioal policy positios. The Cetre for Ecooic Policy Research was established i 1983 as a private educatioal charity, to proote idepedet aalysis ad public discussio of ope ecooies ad the relatios aog the. It is pluralist ad o-partisa, brigig ecooic research to bear o the aalysis of ediu- ad log-ru policy questios. Istitutioal (core) fiace for the Cetre has bee provided through ajor grats fro the Ecooic ad Social Research Coucil, uder which a ESRC Resource Cetre operates withi CEPR; the Esée Fairbair Charitable Trust; ad the Bak of Eglad. These orgaizatios do ot give prior review to the Cetre s publicatios, or do they ecessarily edorse the views expressed therei. These Discussio Papers ofte represet preliiary or icoplete work, circulated to ecourage discussio ad coet. Citatio ad use of such a paper should take accout of its provisioal character. Copyright: Javier Ortega ad Thoas P Tageraas
CEPR Discussio Paper No. 4003 August 2003 ABSTRACT Uiligual versus Biligual Educatio Syste: A Political Ecooy Aalysis* We defie a ecooy coposed of two laguage groups. Value is created through bilateral trade betwee idividuals who ca speak the sae laguage. The value of trade icreases i each participat s level of educatio. We copare a biligual educatio syste, uder which the idividuals who take educatio becoe biligual, with a uiligual syste, uder which the idividuals attedig school ed up speakig the laguage of the politically doiatig group oly. Biligualis is socially optial whe educatio levels are cetralized. I the decetralized equilibriu, idividuals (i) vote over educatio systes aticipatig the future levels of educatio (ii) idepedetly ad siultaeously choose whether or ot to take educatio. We show that i the uiligual syste the returs to educatio for each eber of the doiated group positively deped o the uber of ebers of the sae group attedig school (a badwago effect). Istead, uder biligualis, decisios to take educatio are egatively correlated across groups (a duplicatio effect). For this reaso, the equilibriu educatio levels ay be higher uder uiligualis, ad there ay be uaiity for uiligualis. We fid that laguage coflict, wheever it arises, cosists i a situatio i which uiligualis is supported by the doiat group, while biligualis is defeded by the doiated group. We characterize also the coditios uder which uaiity for biligualis arises. The predictios of the odel are show to be copatible with the alost uaious choice of a biligual Fiish-Swedish educatio syste i Filad (1919-22) ad the choice of a uiligual Frech-laguage syste i Frace (1789-94). JEL Classificatio: I20 ad J15 Keywords: educatio, laguage policies, iorities ad skills
Javier Ortega GREMAQ Uiversité des Scieces Sociales de Toulouse Maufacture des Tabacs, bât. F 21 Allée de Briee F-31000 Toulouse Frace Tel: (33 5) 61 12 85 59 Fax: (33 5) 61 12 86 37 Eail: javier.ortega@uiv-tlse1.fr For further Discussio Papers by this author see: www.cepr.org/pubs/ew-dps/dplist.asp?authorid=139731 Thoas Tageraas The Research Istitute of Idustrial Ecooics (IUI) Box 5501 S-114 85 Stockhol Swede Tel: (46 8) 665 45 26 Fax: (46 8) 665 45 99 Eail: thoas.tageras@iui.se For further Discussio Papers by this author see: www.cepr.org/pubs/ew-dps/dplist.asp?authorid=149970 *We beefited fro discussios with Alai Alcouffe, Raquel Ferádez, Jea Fraysse, Barbara Petrogolo, ad fro coets i seiars at the Uiversitat de Valècia, Uiversité de Toulouse, Uiversidad Pública de Navarra-Nafarroako Uibertsitate Publikoa, IUI, EALE 02 (Paris), LSE, ad SED 03 (Paris). Päivi Erkkilä ad Marjatta Latvus (Library of the Fiish Parliaet), Doh-Shi Jeo, Mika Helader, Eric Mali, ad Keeth Sella helped us gatherig iforatio. Part of this research was doe while the first author was visitig the LSE. The secod author gratefully ackowledges the Ja Wallader ad To Hedelius Research Foudatio for fudig. Subitted 04 July 2003
1 Itroductio I ultiligual coutries, laguage policies are a key deteriat of the developet or the declie of laguages. As stressed by historias of laguage (see aog others, Hagège, 1996) oe crucial copoet behid laguage shift i populatios over geeratios is the choice of the laguage(s) of istructio i school. I other ters, laguages which are ot give the status of ediu of istructio i school ted to be replaced by the laguage used i school. Frace ad Filad provide two iterestig case studies. I late 18th cetury Frace, aroud two thirds of the Frech did ot speak Frech (Grégoire, 1794). 1 The uiligual Frech-speakig educatio syste set up durig the 19th cetury (aog other factors) has lead to a wide laguage shift i Frace, as laguages other tha Frech are ow spoke by aroud 5 percet of the populatio (Ecyclopaedia Britaica, 2002). By cotrast, the biligual Fiish-Swedish educatio syste set-up i Filad after its idepedece i 1917 has bee oe of the factors explaiig the relative good shape of Swedish i coteporary Filad. Ideed, the ative Swedish-speakig populatio has declied to a uch lesser extet i relative ters (fro 11 percet of the total populatio i 1920 to 5.9 percet i 2000), ad has reaied alost costat i absolute ubers (314,000 ative Swedish-speakers i 1920 ad 293,000 i 2000). 2 The objective of this paper is to uderstad the political ecooy of the choice i a ultiligual coutry betwee a uiligual educatio syste ad oe i which ore tha oe laguage is used as ediu of istructio. Our ecooy cosists of a cotiuu of idividuals belogig to two laguage groups iitially uable to couicate. Value is created through bilateral trade betwee idividuals who ca speak the sae laguage. Coditioal o speakig the sae laguage, the atch surplus icreases i each participat s level of educatio. The educatio syste ca be orgaised i two differet ways. Uder a biligual syste, idividuals who choose to atted school lear the laguage of the other group ad keep their ow laguage. I cotrast, uder a uiligual syste, the laguage of the politically doiatig group (the -group) is the uique ediu of istructio, ad thus the doiated group (the -group) ebers who atted school lose their ow laguage. The persoal cost of takig educatio is assued costat across the populatio ad idepedet of the educatio syste. We first show that the biligual syste is socially optial whe educatio levels are cetralised, i.e. whe a beevolet plaer ca choose the educatio level of each idivid- 1 The other laguages spoke were Occita, Alsacia, Fracoia, Basque, Breto, Catala, Fleish, Fraco-proveçal, ad Corsica. 2 Data for 1920 are fro McRae (1997) ad for 2000 fro the Ecyclopaedia Britaica (2003). Accordig to the Research Cetre of Wales (1998), i 1995 the uber of Fis usig Swedish i their everyday life would be aroud 600,000 out of 5 illio. 2
ual. This result is ot surprisig sice uder our assuptios biligualis is techologically superior to uiligualis, i the sese that the agets get access (at a zero additioal cost) to a larger set of potetial parters if they speak both laguages. We the cosider the followig gae. First, aticipatig the future levels of educatio, the educatioal syste is chose so as to axiise the expected utility of the group(s) i power. Secod, the idividuals idepedetly ad siultaeously choose whether or ot to take educatio. We cosider syetric Nash equilibria i which all ebers of each group radoise betwee educatio ad stayig uskilled with the sae probability. A essetial feature of the odel is that idividual decisios of takig educatio geerate exteralities, as the payoff associated to attedig school depeds o the skill level ad the laguages spoke by the potetial parters. Uder uiligualis, the s ever choose to take educatio 3, sice educatio does ot elarge their set of tradig parters. Ideed, ay aget attedig educatio will ed up speakig the laguage of the s, ad thus the s ca avoid payig the cost of educatio. I additio, the returs to educatio for each eber of the -group positively deped o the uber of s who atted school: each tie that a takes educatio, she forgets her iitial laguage, ad thus the other ebers of the group ca keep her as a potetial parter oly if they choose to atted school theselves (a badwago effect). If the cost of educatio is very low (high) ad/or the -group is sufficietly sall (large), all (oe of) the s take educatio. For iterediate values of these two paraeters, both equilibria co-exist. Uder biligualis, the badwago effect is abset, sice obody loses her ow laguage whe attedig school. I cotrast, this syste is characterised by egative exteralities i the decisios to take educatio across groups: ay eber of oe group who chooses to atted school becoes biligual ad thus becoes a additioal parter for the ebers of the other group who do ot atted school (a duplicatio effect), reducig the icetives for educatio. The egative ature of the exteralities explais why ultiple equilibria, whe they arise, are characterised by all the ebers of oe group ad oe of the other takig educatio. Whe the equilibriu is uique, the oly group which udertakes educatio (if ay) is the sallest group. Cocerig the choices of both groups betwee the two educatio systes, the odel delivers three iterestig results. First, our odel predicts that the s ever support uiligualisiasituatioiwhichthes favour biligualis. I other words, the oly type of laguage coflict that arises as a equilibriu outcoe is oe i which the s push for a uiligual syste i its ow laguage, while the s support biligualis. The ituitio goes as follows: whe educatio is very expesive, the s ever take educatio uder ay 3 Uless we are i the trivial case i which the iproveet i productivity associated to takig educatio is itself higher tha the cost of educatio. 3
syste, while the s ay take educatio oly uder biligualis due to the badwago effect. The, the s support uiligualis because they ca beefit fro the other group s educatio, ad the s prefer a syste i which they ca avoid takig educatio. This is a iterestig result sice it does ot rely o ay direct utility ejoyed fro speakig oe s ow laguage. A secod iportat result is that despite the techological advatage assued here for biligualis, uaiity for uiligualis is a equilibriu outcoe i soe cases. The ituitio coes fro the differet ature of the exteralities: as exteralities are positive uder uiligualis, the equilibriu educatio levels ay ed up beig higher i a uiligual syste, ad both groups ay prefer this syste if educatio is ot too expesive. 4 O the cotrary 5, there is uaiity for biligualis if educatio is cheap ad the size of the -group is sufficietly large. Reeber that the s ever get educated uder uiligualis, while they ay atted school i a biligual syste. The, the s prefer a biligual syste, sice they ca avoid payig the cost of educatio, ad, as the -group is big, a large proportio of potetial parters get skilled. The s alsoprefera biligual syste: if educatio is cheap, bearig the cost of educatio is copesated by the fact that eetig aother is uch ore likely tha eetig a. 6 Next, we address the issue of failure i political decisio-akig, i.e. we study uder which circustaces the political decisio process leads to the adoptio of the wrog type of educatio syste. For this purpose, we defie a ew optiality bechark, correspodig to the socially optial educatio syste with decetralised educatioal choices. We show that political failure ay arise whe the s are the rulig group i the political process (biligualis chose too ofte) ad whe the s are the rulig group but costitute a iority (uiligualis chose too ofte). The theoretical part of the paper is copleted with a aalysis of copulsory educatio. More precisely, we study whether agets ca alleviate the udereducatio outcoe resultig fro coordiatioal failures by choosig to itroduce copulsory educatio. We show that copulsory educatio is chose as a solutio to udereducatio oly i a part of the paraeter space where this proble arises. Fially, we show that the predictios of the odel for the Fiish ad the Frech case are copatible with the observed outcoes. I Filad (1919-1922), the Swedish-speakig 4 More precisely, the presece of the badwago effect leads to positive aouts of educatio i the uiligual syste, while uder biligualis obody gets educated. If educatio is ot too expesive, the s prefer to pay the cost of educatio rather tha reai ueducated ad are able to trade with a relatively sall uber of parters. 5 I additio to these situatios, i soe cases the agets are idifferet betwee the two systes, ad for soe zoes of the paraeter space the choice betwee uiligualis ad biligualis is ideteriate for soe idividuals, i.e., soe of the equilibria uder uiligualis are preferred to their biligual couterpart, while others are doiated. 6 Uaiity for biligualis arises also i situatios i which the s do ot get educated uder either syste, ad the educatio level of the s is higher uder biligualis. 4
group was sall (11.6% of the populatio i 1910), ad the biligual Fiish-Swedish educatio syste was approved by a overwhelig ajority 7, with the etire support of the Swedish-speakig side ad a very large support of the Fiish-speakig group. As see above, our odel predicts that uaiity for biligualis ca be reached if the size of the -group (here, the Fiish-speakig) is sufficietly large. I Frace (1789-1794), the Frech-speakig group was sall (aroud oe third of the populatio) ad it sees reasoable to assue that the cost of educatio was high. A uiligual Frech-speakig syste was chose whe power was uder the cotrol of the otagards, radical jacobis revolutioaries with the support of the Parisia sas-culottes (see Furet, 1988), so the s favoured uiligualis. The positio of the o-frech speakig groups eeds further aalysis: while a series of federalist rebellios took place i 1793 i the ai o-frech speakig tows (Bordeaux, Lyo, Marseilles, ad Toulouse), it is uclear to what extet laguage was a iportat issue. Our odel predicts that whe the -group is sufficietly sall ad the cost of educatio sufficietly high, either there is uaiity for biligualis or a laguage coflict i which the s support uiligualis. Other papers i the literature have odelled laguage ad/or laguage acquisitio. Church ad Kig (1993) shows i a gae-theoretic settig that the idividual decisios of laguage acquisitio ca be iefficiet. Laiti (1994) uses also gae theory to study why state-iduced coordiatio o a atioal laguage is difficult to achieve i ultiligual coutries. Joh ad Yi (2001) develops a dyaic settig to provide a explaatio of the factors leadig to a declie or a developet of differet laguages. 8 Our ovel cotributio to the literature is the odellig of the specific role of schoolig, together with the aalysis of the political ecooy of the decisios cocerig educatio systes. 2 The odel Cosider a coutry ihabited by a cotiuu of citizes, oralised to uity. I the coutry there are two laguage groups, ad, of sizes M (0, 1) ad N =1 M, respectively. Iitially, the s speakish ad the s ish. s ads are uable to couicate uless they lear to speak a coo laguage. A fractio µ (µ )ofthes (s) take educatio ad becoe skilled. The rest reai uskilled. µ ad µ are edogeously deteried. Value is created through bilateral trade betwee idividuals. Each citize is atched exactly oce with every other citize. Two uskilled who eet ad trade gai oe uit of surplus each. If oe is skilled ad the other uskilled, surplus icreases to 1+σ for each. 7 see Eduskuta-Riksdag (1920). 8 Other papers studyig laguage are Lazear (1999) ad Sait-Paul (2001). 5
A atch betwee two skilled creates a surplus of 1+2σ for each. 9 Trade occurs if ad oly if the two potetial tradig parters are able to couicate, i.e. speak a coo laguage. If they caot couicate, there is o trade ad each obtais zero surplus. Returs to educatio are two-fold. Takig educatio iplies becoig skilled, which icreases the value of trade as described above for all agets with which a skilled perso trades, hece there are positive skill exteralities i educatio. Schoolig also ivolves laguage traiig, the type depedig o educatioal syste. This paper copares a uiligual to a biligual educatioal syste. The persoal cost c of takig educatio is assued costat across the populatio ad idepedet of the educatioal syste. 2.1 The uiligual educatio syste Uder the uiligual syste, ish 10 is the uique laguage of istructio. The s who atted school becoe skilled ad keep their iitial laguage. The s who take educatio becoe skilled, lear ish ad lose their iitial laguage. Ideed, as show by historias (see e.g. Hagège, 1996, for the case of Frace) oe crucial factor behid laguage shift i populatios over geeratios is the choice of the laguage(s) of istructio i school. I other ters, laguages which are ot give the status of ediu of istructio i priary school ted to be replaced by the laguage used i school. The expected utility of takig educatio uder a uiligual syste, give expected educatio shares µ =(µ,µ ) is: 11 U ui (µ) =M[(1 + 2σ)µ +(1+σ)(1 µ )] + N(1 + 2σ)µ c. (1) Becoig educated eas havig ish as sole laguage ad a high skill level. The skilled trade with all the s, the value of which is give by the first ter i brackets. The first part is the value of tradig with the skilled, the secod part the value of tradig with the uskilled. The skilled trade also with those of the s who have take educatio. The value of this trade is give by the secod ter i brackets. Fro this is to be subtracted the cost of educatio. Each skilled idividual uabigously beefits fro ayoe else takig educatio. There are two reasos. First, icreasig the skill level of oe aget ehaces the value of trade for all tradig parters through the skill exterality. Secod, the s ad skilled s beefit fro additioal s takig educatio through a expasio of their 9 This eas that the retur to skill, the value added of icreasig the skill level of oe of the tradig parters, is costat ad give by σ. 10 The assiget of the doiat role to the group is arbitrary ad without loss of geerality. So far we have said othig about the relative sizes of the two groups or the aout of skilled belogig to each. Nor have we described the political process by which the educatioal syste is chose. 11 There is o eed to ake a distictio betwee s ads who take educatio sice they speak sae laguage ad have idetical skill levels subsequet to becoig educated. 6
set of tradig parters, a positive couicatio exterality. 12 A uskilled trades oly with other uskilled s. Hece, the expected utility for a of stayig uskilled is U ui (µ) =N(1 µ ) (2) uder the uiligual syste. The uskilled lose fro others takig educatio. This is a exaple of a egative couicatio exterality, as those who becoe educated o loger are able to trade with the reaiig uskilled s. A uskilled iproves also her situatio whe other agets take educatio: while she trades with exactly the sae people, soe of the atches becoe ore productive: U ui (µ) =M[(1 + σ)µ +(1 µ )] + N(1 + σ)µ. (3) 2.2 The biligual educatio syste Uder the biligual syste, all those who take educatio becoe biligual, hece able to couicate with the etire populatio. Cosequetly, the skilled trade with everybody. The expected utility of takig educatio uder a biligual syste give expected educatio shares µ =(µ,µ ) is: U bi (µ) =M[(1 + 2σ)µ +(1+σ)(1 µ )]+ N[(1 + 2σ)µ +(1+σ)(1 µ )] c. (4) The first ter i brackets is the value of tradig with the s ad the secod ter the value of tradig with the s. As was the case uder the uiligual syste, ayoe who has take educatio beefits fro all other doig so. This tie the beefit is etirely due to the skill exterality, as the educated are able to trade with everybody idepedetly of her laguage backgroud. The expected utility of stayig uskilled uder the sae coditios for ayoe belogig to the asses is: U bi (µ) =M(1 + σ)µ + N[(1 + σ)µ +(1 µ )]. (5) The differece betwee this expressio ad (2), which idetifies the value of beig ueducated uder the uiligual syste, is that biligualis eables the uskilled stoaitai tradig relatios with all other s ad are ow able to trade with the skilled s. The egative couicatio exterality that arises uder the uiligual syste is reoved uder the biligual syste. 12 It is possible to view a laguage as a etwork defiig the set of tradig parters. With this teriology, the couicatio exterality would be the equivalet of a etwork exterality. Everybody belogig to the etwork beefits (loses) fro additioal people joiig (leavig) the etwork. 7
The expected utility of the uskilled s uder a biligual syste is the sae that i the uiligual case, as the uskilled s couicate with ad trade oly with those who kow how to speak ish. Hece, 2.3 Equilibriu U bi (µ) =M[(1 + σ)µ +(1 µ )] + N(1 + σ)µ. (6) The tiig is as follows. First, aticipatig the future levels of educatio, the educatioal syste is chose so as to axiise the expected utility of the group(s) i power. Secod, the populatio idepedetly ad siultaeously choose whether or ot to take educatio. We cosider without loss of geerality syetric Nash Equilibria i which all ebers of each group radoise betwee educatio ad stayig uskilled with the sae probability. 3 Equilibriu educatio levels 3.1 The uiligual educatio syste By subtractig (2) fro (1), we obtai the idividual s et beefit of takig educatio uder a uiligual syste: U ui (µ) =[Mµ + Nµ ](1 + σ)+m(1 µ ) N(1 µ )+[M + Nµ ]σ c. (7) We ca distiguish betwee three effects. First, there is a couicatio effect which alters the set of tradig parters. Uder the uiligual syste, the couicatio effect ca further be broke ito three separate parts. By takig educatio, the skilled is ow able to trade with the skilled s ad the other skilled s. That effect is captured by the first ter. Further, she is able to trade with the uskilled s, the effect of which is captured by the secod ter. Ufortuately, the skilled ca o loger trade with the uskilled s, which is captured by the third ter. Educatio icreases the value of trade through icreased skills. This skill effect is the fourth ter. It is give by the argial value of educatio σ ties the fractio of people with which the skilled trades, the s ad the other skilled s i this case. Fially, there is a cost effect represeted by the last ter. Equatio (7) displays a iportat feature which turs out to be crucial to the uderstadig of the prefereces over educatio syste of two laguage groups. A icrease i the uber of s that take educatio reiforces both the couicatio ad the skill effect, as ore people speak ish ad less people speak ish. Thus, the educatioal choice of a geerally depeds o the educatioal choice of her peers. The icetive for takig educatio is strog if ay other s take educatio. There is uch less poit i takig educatio if the other s choose to reai uskilled. 8
The et beefit U ui (µ) =[M + Nµ ]σ c (8) of becoig skilled for a eber of the asses is obtaied by subtractig (3) fro (1). Here, oly the skill ad cost effects show up, sice the s dootleartospeakish ad the set of tradig parters does ot chage. The badwago or sowball effect i educatioal choice of the s soeties gives rise to ultiple equilibria. I additio to the possibility of two extree equilibria i which either all or oe of the asses take educatio, there ay exist a ixed equilibriu. 13 However, as the icetive for takig educatio is positively correlated across groups: Propositio 1 Uder the uiligual educatio syste, equilibriu educatio levels are positively correlated across laguage groups i the followig sese: i the cases with ultiple equilibria high (low) educatio levels aog the s are coupled with high (low) educatio levels aog the s. Proof. Let z ui =(z ui,z ui We eed to establish that z ui they do. y ui U ui thus z ui ) ad y ui =(y ui >y ui ad y ui,y ui >zui ) be two distict equilibria of the gae. caot siultaeously hold. Suppose >zui ui 0 U (yui ) 0. U ui(µ)/ µ > 0 U ui(zui ) > (y ui ) for z ui >y ui. Hece, z ui >y ui ad y ui >z ui U ui (z ui ) > 0 ad =1, which cotradicts yui >zui. Let us cosider i ore detail the types of possible equilibria that ca potetially arise. Figure 1 characterises the set of equilibria i (c σ, M) space for the c>σcase. The 13 This ustable equilibriu is soeties referred to as a tippig equilibriu, a ter coied by Schellig (1978). 9
reaso for cosiderig this subspace will becoe apparet whe we tur to the political aalysis i the ext stage. 14 Moreover, we restrict attetio here to the σ>1case, that is, whe the argial beefit of icreasig the skill level is larger tha the argial beefit created whe two uskilled eet ad trade. At this stage this is purely for expositioal purposes. The first thig to otice is that the s ever take educatio uder the uiligual syste wheever c>σ. As there is o couicatio effect at play for this laguage group, the educatioal choice depeds etirely o the agitude of the skill effect. If c>σ, the skill effect is ever sufficietly strog to iduce the s to take educatio, eve if all the s should choose to take educatio. For the s, educatioal choice higes crucially o the relative sizes of the two laguage groups ad potetially o the choices of the other s. If N is sall, or equivaletly, M is large, it does ot atter what the other s do. By takig educatio, the set of tradig parters is sigificatly expaded ad so the couicatio ad skill effects are both strog. Hece, if the uber of s exceeds soe lower threshold M ui 1,alls take educatio, ad (1, 0) is the uique equilibriu. Coversely, if the uber of s is suffietly large, the badwago effect i educatio becoes iportat. Suppose oly a few s take educatio. I this case the skill effect ad couicatio effects are weak, hece it is uprofitable to take educatio. If, o the other had, a large proportio of the s take educatio, the skill ad couicatio effects are strog, hece it becoes very profitable to take educatio. There are ultiple equilibria. As educatio becoes icreasigly expesive, the exteralities becoes icreasigly iportat for educatioal choice. Whe educatio is very expesive (c >1+σ), positive educatio levels ca be sustaied if ad oly if the exterality i educatio is very strog, i.e. the size of the group drops below a upper threshold M ui 2. Evetually, educatio becoes so expesive (c >1+2σ) that obody ca afford to take educatio. 3.2 The biligual educatio syste Subtract (5) fro (4) to get U bi (µ) =M(1 µ )+σ c, (9) the et beefit of takig educatio for the uskilled uder the biligual syste. The first ter is the couicatio effect. By takig educatio, the expads her set of tradig parters to iclude the uskilled s. The skill effect is siply equal to σ sice the skilled trade with the whole populatio ad there are costat returs to skill. The cost of 14 Whe c<σ, a plethora of subcases arise. The iterested reader could cosult the appedix for a full characterisatio of the equilibria. 10
educatio is give by c. Everythig is syetric for the s. Hece, the et beefit for a of becoig educated is U bi (µ) =N(1 µ )+σ c. (10) As opposed to the situatio uder the uiligual syste, the educatio level i the populatio ow has a egative effect o the idividual icetive for takig educatio. Whe ore people of the other group becoe educated ad lear to speak a perso s ative laguage, it becoes less iportat for that perso to lear the other laguage. Educatio weakes the couicatio effect of educatio, which we shall label a duplicatio effect. Whe it coes to tradig opportuities, there is o poit i both groups speakig both laguages. The equilibriu levels of educatio are depicted i Figure 2 above. Suppose all ebers of oe group take educatio, so that the duplicatio effect copletely eradicates all couicatio effects. I this case the icetive for takig educatio depeds etirely o the skill effect σ relative to the cost c of educatio. If c<σ, the skill effect aloe is sufficiet to iduce people to take educatio, hece the uique equilibriu educatio levels are (1, 1) i this case. If c>σ, the skill effect provides isufficiet icetives for becoig skilled, hece the couicatio effect coes ito play. The couicatio effect is stroger for the saller tha the larger group sice the set of tradig parters subsequet to becoig skilled is expaded ore for the forer tha the latter group uder a biligual syste. 11
Cosequetly, the saller group has a stroger icetive for takig educatio tha the larger group, all other thigs equal. If educatio is quite cheap (c <0.5+σ) ad the groups do ot differ too uch i size, it ay be oe group or the other that takes educatio i equilibriu. It is also possible that a positive fractio of the ebers i each group takes educatio. 15 If the groups differ at lot i size, however, the positive couicatio effect is ever sufficiet to reder educatio profitable for the largest group. Hece, if the cost of educatio is sufficietly sall ad oe group is very sall copared to the other, there is a uique equilibriu i which the sallest group becoes educated ad the largest does ot. The iportace of relative group size becoes eve ore proouced whe the cost of takig educatio is quite large. As the cost of educatio icreases (c >0.5 +σ), a stroger ad stroger couicatio effect is required so as to aitai the icetives for becoig educated, i.e. oly whe groups vary a lot i size will oe of the fid it beeficial to take educatio. If the groups are quite equal i size, the couicatio effect is isufficiet for both groups, hece they both reai uskilled. Fially, whe the cost of educatio becoes too large, (c >1+σ), o oe will ever choose to take educatio uder the biligual syste. We ed this sectio by statig ad provig a propositio regardig a feature of the biligual syste which should be obvious fro ispectio of Fig. 2: Propositio 2 Uder the biligual educatio syste, equilibriu educatio levels are egatively correlated across laguage groups i the followig sese: for the cases with ultiple equilibria, high (low) educatio levels aog the s are coupled with low (high) educatio levels aog the s. Proof. Cosider z bi =(z bi,zbi ) ad ybi =(y bi,ybi ) two distict equilibria of the gae. z bi >y bi ad z bi >y bi caot siultaeously hold. Suppose they do. y bi <z bi 1 U bi(ybi ) 0. U bi(µ)/ µ = N U bi(zbi ) < U bi(ybi ) for z bi >ybi. Hece, z bi >ybi ad zbi >ybi 4 Welfare U bi (zbi ) < 0 ad thus z bi =0, which cotradicts ybi <zbi. This sectio cosiders the welfare properties of the uiligual ad biligual educatio systes. Defie expected welfare uder educatioal syste s {ui, bi} by W s (µ) =M[µ U s (µ)+(1 µ )U s (µ)] + N[µ U s (µ)+(1 µ )U s (µ)]. 15 As was the case uder the uiligual syste, ay iterior equilibriu that arises uder the biligual syste is ustable. 12
As a first step, keep educatio levels exogeously fixed at µ =(µ,µ ) ad copare utility uder the two systes, group by group. Subtract (1) fro (4) to obtai the et beefit of the skilled of havig a biligual educatio syste, all other thigs held equal: U bi (µ) U ui (µ) =N(1 + σ)(1 µ ) 0. (11) The skilled ow beefit fro beig able to trade with the uskilled asses fro the group. Subtract (2) fro (5) to obtai the et beefit of the uskilled s of switchig fro a uiligual to a biligual syste, all other thigs held equal: U bi ui (µ) U (µ) =[Mµ + Nµ ](1 + σ) 0. (12) This group beefits a lot because the set of tradig parters expads to iclude the skilled of both laguage groups. The s are idifferet betwee the two educatio systes, all other thigs held equal, as their set of tradig parters is uaffected by a chage i educatio syste: U bi (µ) U ui (µ) =0 (13) Of course, educatio levels are ot exogeously give, hece we caot o the backgroud of the above coparisos coclude that the biligual is superior to the uiligual syste fro a welfare poit of view. We eed to adjust for educatio levels. 4.1 Full cetralisatio syste Suppose there exists a beevolet social plaer who is able to select the level of educatio that axiises welfare uder each syste. Propositio 3 Uder full cetralisatio, the biligual syste yields higher expected welfare tha the uiligual syste. The welfare axiisig educatio levels (x,x ) are (i) (1, 1) if c<2σ; (ii) (1, 0) if c (2σ, 2(1 + σ)) ad M > ax{1/2; c/2 σ}; (iii) (0, 1) if c (2σ, 2(1 + σ)) ad N > ax{1/2; c/2 σ} ad (iv) (0, 0) if c>1+2σ, M, N < i{1; c/2 σ}. Proof. The biligual syste outperfors the uiligual syste: Write x s =(x s,x s ) welfare axiisig educatio levels uder s. (11)-(13) o-egative yield W bi (x ui ) W ui (x ui ). By optiality of x bi uder the biligual syste, we have W bi (x bi ) W bi (x ui ). Addig the two iequalities produces W bi (x bi ) W ui (x ui ). Socially optial educatio levels: By differetiatig (4)-(6) with respect to µ ad µ ad pluggig i (4)-(6), it is easily verified that (subscripts deote partial derivatives throughout): Wµ bi (µ) =M(2N(1 µ )+2σ c) Wµ bi (µ) =N(2M(1 µ )+2σ c). 13
(i) follows directly fro Wµ bi M(2σ c) ad Wµ bi N(2σ c). (iv) follows fro Wµ bi 2M(N + σ c/2) ad Wµ bi 2N(M + σ c/2) ad the fact that M<c/2 σ ad N =1 M<c/2 σcasiultaeously hold if ad oly if c>1+2σ. We fially prove (ii). The proof of (iii) follows fro a syetric arguet ad is oitted. Note first that M<1ad M>c/2 σcasiultaeously hold if ad oly if c<2(1 + σ), hece the upper liit o c. LetN(1 µ )=M(1 µ )=c/2 σ. I the relevat paraeter space, Wµ bi ( µ, µ )=Wµ bi ( µ, µ )=0, Wµ bi (µ) < 0 for all µ > µ, Wµ bi (µ, 0) > 0, Wµ bi (µ) > 0 for all µ < µ ad Wµ bi (µ, 1) < 0, hece there are at ost three cadidates for a social optiu: (1, 0), (0, 1) ad ( µ, µ ). W bi (1, 0) W bi (0, 1) = 2(M 0.5)(c 2σ) ad W bi (1, 0) W bi ( µ, µ )=(M 0.5 +σ)(c 2σ) iply W bi (1, 0) >W bi (0, 1) ad W bi (1, 0) >W bi ( µ, µ ) i the relevat paraeter space. The cetral plaer would always choose a biligual syste if able to fully cotrol eductioal levels of the populatio. It is ot hard to uderstad why. For give educatio levels, ore people couicate, hece trade, uder a biligual tha a uiligual syste. As welfare is icreasig i trade everythig else equal, it iediately follows that the biligual is better tha the uiligual syste. The propositio also describes optial educatio levels. The expressios look coplicated at first, but really are quite ituitive. The welfare optiisig educatio levels uder the biligual syste are draw i Figure 3 below. Educatio levels are decreasig i the cost of takig educatio. Whe educatio is cheap, it is socially optial for the whole populatio to becoe educated. A icrease i the cost of becoig skilled beyod a certai poit (c >2σ) reders suboptial that everybody takes educatio. However, to axiise the total value of educatio it is i- 14
portat that couicatio is hurt to the lowest possible extet. Full couicatio is preserved if all the ebers of oe group get educated, ad the cheapest way of attaiig this is by havig the ebers of the sallest group attedig school. This is illustrated i Fig. 3, where the s are the oes who becoe educated whe the s are sufficietly large i uber (M >ax{0.5,m 1 })adthes becoe educated whe the s are sufficetly sall i uber (M <ax{0.5,m2 }). Whe educatio is very costly, ad the groups are sufficietly equal i size, it is too costly for society to achieve couicatio, hece o group gets educated. This is the area i Fig. 1 for which c>1+σ ad M (M 2,M ). 1 4.2 Decetralised educatioal choice I reality, of course, o cetral plaer ca perfectly cotrol the aout of effort studets put ito their studies, eve i a syste with adatory educatio. To capture this degree of freedo, cosider therefore a fully decetralised educatio syste i which the choice whether to becoe educated or ot is fully delegated to the idividuals. Let y bi ad y ui be the equilibriu levels of educatio uder this decetralised educatio syste. It is still the case that W bi (y ui ) W ui (y ui ), but it is o loger ecessarily true that W bi (y bi ) W bi (y ui ), hece the welfare iplicatios are uclear ad cotiget upo equilibriu educatio levels. As previously show, ultiple equilibria soeties arise. I odels with ultiple equilibria, odel predictios geerally deped o the equilibria that are uder cosideratio. We focus o results that hold for all coparisos of stable equilibria. For exaple (foral defiitios are give i the appedix), a group weakly prefers the biligual to the uiligual syste if the ebers are ever worse off i ay stable biligual equilibriu tha ay stable uiligual equilibriu ad strictly better off i at least oe stable biligual equilibriu tha i all stable uiligual equilibria. Soe of our results deped o the exclusio of the iterior ustable equilibria, but ay do ot. I the subsequet aalysis, we discuss the atter of equilibriu selectio wheever relevat. Figure 4 characterises the optial decetralised educatio syste for σ>1. Wheever c<σ, the decetralised biligual syste geerates the optial aout of educatio for both groups ad, cosequetly, is the socially optial oe. As the cost of takig educatio icreases above σ, educatio systes ay fail to create sufficiet icetives for takig educatio. Whe educatio is ot too expesive, society prefers the ajority group to becoe educated. Whe the s are i ajority, this leads to the adoptio of a biligual syste as this is the oly oe that produces ay icetives for that group to take educatio. 15
The figure vividly deostrates how the biligual syste ay cease to be the optial oe oce educatioal choice becoes decetralised. Whe the cost of takig educatio is sufficietly high ad the differeces i group size rather sall, the biligual syste fails to produce sufficiet icetives for takig educatio. The couicatio effects siply are ot strog eough. Uder the uiligual syste, o the other had, the badwago effect is strog eough to sustai positive educatio levels, eve if educatio is costly. As couicatio ad skills are axiised uder the uiligual syste, i this case it is the socially optial of the two. This is ot to say that the badwago effect is always beeficial to society. Whe the s are i a large ajority ad educatio very expesive, the badwago effect ay trap the ajority groups i iefficietly high educatio levels. To overcoe the couicatio barrier, it is always the sallest ad ot the largest group that should be educated. I this case educatio is so costly that it is worse for society to have the wrog group tha o oe at all to becoe skilled. I order to avoid this fate, it is better to ipleet a biligual syste. 5 The choice of educatio syste Whe the cost of educatio is very low, all ebers of the populatio are better off if everybody else takes educatio, eve if it eas oeself havig to take educatio. Oe way of guarateeig that educatio levels are axiized whe the cost of takig educatio is sall, is to vote for a biligual syste. 16
Propositio 4 If c<σ, all groups prefer the biligual to the uiligual syste. Proof. For c<σ, (1, 1) is the uique equilibriu uder the biligual syste, as show i the appedix. U bi (1, 1) = U ui (1, 1) = 1 + 2σ c. To coplete the proof, we show that all groups prefer the (1, 1) equilibriu to ay other equilibriu uder the uiligual syste wheever c<σ. Copare (1, 1) uder a uiligual syste to a arbitrary equilibriu y ui = (y ui,y ui ) (1, 1). All those who would reai skilled uder a alterative equilibriu prefer the (1, 1) equilibriu: U ui (1, 1) U ui (y ui )=M(1 y ui )σ + N(1 y ui )(1 + 2σ) > 0. All those who would be uskilled uder a alterative equilibriu prefer the (1, 1) equilibriu, too: U ui (1, 1) U ui (y ui )=1 N(1 y ui )+2σ c>0. U ui (1, 1) U ui (y ui )=N(1 y ui )(1 + σ)+m(1 y ui )σ + σ c>0. Figures 5 ad 6 characterise the prefereces of the s ad s, respectively, regardig educatio syste for c>σ. This is the case for which duplicatio effects start playig a role for educatioal choice uder the biligual syste. I regio I, the s are so doiatig i size relative to the cost of educatio, that the badwago effect i educatio is too weak to carry ay weight i the educatioal choice of the s uder the uiligual syste. Istead, the skill ad couicatio effects are sufficetly strog to lead all s to take educatio uder both systes. The skill effect is too weak uder the uiligual ad the couicatio effect too weak uder the biligual to geerate sufficiet icetives for the s to take educatio uder ay of the systes. I equilibriu, therefore, all ed up speakig ish ad oly the s beig skilled, o atter which syste is chose. Hece, the s ads are both idifferet betwee the two systes i regio I. 17
Regio II is uch like regio I, except ow the s have becoe sufficiet i uber relative to the cost of educatio, for badwago effects to becoe key i shapig the icetives for takig educatio uder the uiligual syste. The s still do ot take educatio uder either syste, hece opt for the syste that axiises the equilibriu aout of educatio aog the s. By selectig the biligual syste they avoid the risk of the s beig trapped i a low educatio equilibriu, while aitaiig the icetive for the s to becoe educated uder the biligual syste through the strog couicatio 18
effect. The s are the oes who have to carry the cost of educatio uder both systes. However, tradig with the s is so iportat that they wat to avoid edig up i a low educatio equilibriu. Hece, the s too opt for a biligual equilibriu. I regio III, the size of the group has icreased eve further relative to the cost of takig educatio. Now, either the cost of takig educatio is too high, or the laguage groups too equal i size to geerate a sigificat couicatio effect for ay of the groups uder the biligual syste. Thus equilibriu educatio levels are zero for both groups uder the biligual syste. Uder the uiligual syste the badwago effect is strog eough to sustai positive educatio levels uder the uiligual syste. Hece, the s go for that syste. For the s, o the other had, thigs are ot so siple. Whe the cost of takig educatio is ot so high (Regio IIIa), the high educatio equilibriu is still better tha the low educatio equilibriu, hece the s prefer the uiligual syste, too.16 Whe the costs icrease eve further (Regio IIIb), the s chage opiio ad prefer the biligual syste istead. I regio IV, the cost of takig eductio has becoe so large that equilibriu educatio caot be sustaied for ay group uder ay syste. Uder the uiligual syste, educatio is either too expesive, or the badwago effect o couicatio too weak to sustai positive educatio levels. Hece, equilibriu educatio levels are zero for both groups uder both systes hee everybody is idiffergrt as to the choice of educ1(r)-10atio syste. I rgrio V.1(r)-10duc1(r)-10atio is so cheap ad the size group of the so large that both groups would prefer the s to becoe educated uder a biligual syste - eve the s theselves, owi to the stro skill extery. Uer the uiligual syste, the wro group for sure is provided with the icetives for takig educatio. Hece, both groups prefer the biligual syste. I regio VI, the s are i sufficiet size a the cost of educatio sufficietly low to geerate a sufficiet icetive for the s to take educatio uder the biligual syste, give that the s do ot take educatio. Now, however, the s would prefer the other group to bear the cost of educ1(20.2(a)-10.1(t)0(i)-20.3(o)-0.1(.)-450.3(al)-10.3(l)-330.3(t)-10(he)]tj/f71tf15.07 pull i favour of a uiligual equilibriu. However, owig to the also a equilibriu that obody at all takes educatio, i which fer the biligual syste, after all. As we caot say aythig about e uiligual equilib is ore likely, the pces of the s are fial case. This is ot to say that the prefereces of the s ecessarily the regios (VIa-c), the s are i sufficiet uber that the s opt s are better off uder the zero educatio biligual tha the iterior uiligual equilibriu. Ituitively, equilibriu educatio levels are isufficiet to cover the cost of educatio for each idividual. Hece, if we iclude iterior equilibria ito the copariso, the prefereces of the s becoe ideteriate i this area. 16 This result is ot robust to the iclusio of iterior equilibria. 19 The
for a biligual syste so as to geerate icetives for the for takig educatio. 17 If the s are i ajority, however, ad educatio is cheap (regio VId) they would prefer to be skilled theselves tha the others to be skilled, which i tur is preferred to o oe takig educatio at all. Hece, i this rage the prefereces of the s are ideteriate. Havig, deteried the prefereces of the two groups regardig educatioal syste, we eed to copare how well they atch across the two groups to see whether political digressio ever arises. Figure 7 is a bled of Figures 5 ad 6. Perhaps a bit surprisigly, there is soeties uaiity for the uiligual syste, i.e. the s are perfectly willig to give up their ow laguage ad the s perfectly happy to accoodate their wishes. Uaiity for the uiligual syste occurs i cases i which the cost of takig educatio is sufficetly high ad the groups sufficietly equal i size to reder the couicatio effect isufficiet to geerate icetives for takig educatio uder the biligual syste, but where the group is sufficietly large to geerate a strog badwago effect ad thereby potetially positive educatio levels uder a uiligual syste. As educatio i this case is ot too expesive, it is better to take educatio ad trade with other skilled s tha to save o the cost of educatio ad trade oly with uskilled s, which would be the guarateed outcoe uder the biligual syste. Of course, if the s prefer the uiligual to the biligual syste, so do the s, as the s do ot eve have to bear the cost of educatio, but evertheless beefit fro icreased trade with the s. 17 Regio VIb becoes ideteriate for the case of the s if we iclude iterior equilibria. I that case the s would be better off uder the (1, 0) uiligual equilibriu tha the ixed biligual equilibriu, which i tur is preferred to the o-educatio uiligual equilibriu. 20
The observatio that the s always prefer the uiligual syste if the s doso,has the iplicatio that the situatio will ever occur i which the s propagate i favour of a uiligual syste ad the s argue for a uiligual syste. The oly political tesio possible is the situatio i which the doiatig () group wats to ipleet its ow laguage i a uiligual syste whereas the doiated () group opts for a biligual syste. This happes i situatios siilar to the oe above, aely whe equilibriu levels are zero i the biligual syste, but the badwago effect sufficiet to geerate a potetial for positive educatio levels uder the uiligual syste. The s go for a uiligual syste, owig to the possibility of catchig the s i a high educatio equilibriu, whereas the the s go for a biligual syste, precisely i order to prevet the sae thig fro happeig. The diffece bewtee this ad the uaiity case is that the cost of educatio ow is so high that the s are better off stayig uskilled ad tradig with other uskilled s oly tha to take the cost of educatio ad trade with the other skilled s ad the s. I additio to the possibilities above, there are cases i which both groups agree o a biligual syste. This exclusively happes whe the s are i ajority ad the cost of educatio low. I this case it is iportat for both groups to geerate strog icetives for the s for takig educatio. This ca oly be achieved i a biligual syste. We ext tur to a exaiatio of the welfare properties of political decisio-akig. This is doe by coparig the outcoes of the political process (Fig. 7) to the socially optial educatio syste with decetralised educatioal choice (Fig. 4). I particular, we address the issue of political failure. Which, if ay, are the circustaces uder which the political decisio-process leads to the adaptio of the wrog educatio syste? For a substatial part of the paraeter space for which welfare rakigs ca be ade, there is uaious agreeet o the socially optial educatio syste, i.e., both groups beefit fro itroducig the socially optial syste. This happes i particular whe educatio is ot particularly expesive. Whe discourse arises, it is ot ecessarily so that the syste preferred by the ajority is the socially optial oe. If the s happe to be i ajority, the socially optial syste is always chose. Whe the s are i ajority, o the other had, they ted to select the biligual syste i circustaces uder which the uiliual syste would actually be better. They do so i order to avoid beig caught i a, to the, ufavourable higheducatio situatio. If we iterpret ajority rule to be deocracy, we coclude that deocracy leads to biligualis beig chose too ofte, with too low educatio levels as the uevitable result. Cosider istead the erits of iority rule. If the s are the iority rulers, they choose the socially sub-optial biligual syste too ofte, for the sae reaso as before. O the cotrary, if the doiatig group is the iority ruler, the socially optial rule is chose, uless the s are i very sall uber, i which case the uiligual syste is 21
adopted despite the biligual syste beig the optial oe. The s go for the uiligual syste hopig to be able to catch the s i a socially sub-optial equilibriu with too ucheducatioopartofthes. Note fially that ideteriacy i the political odel ot ecessarily is a political failure. For a large part of the paraeter space for which the differet groups have o clear prefereces, it is also true that the differet systes caot be welfare raked, either. The proble lies i the exteralities that follow as a result of decetralised educatioal choice. 6 Copulsory educatio So far we have assued educatioal choice to be fully decetralised to idividuals. Cosiderig the fact that decetralised educatio systes ted to create either too weak icetives, or icetives for the wrog group to becoe educated, it is pertiet to ask whether these probles ca i ay way be alleviated. Fig. 8, which is a bled of Fig. 7 ad Fig. 3, shows that decetralised educatio choice leads i ay cases to udereducatio with respect to the optial educatio levels. Oe potetial reedy is of course copulsory educatio. I this way everybody coordiates o the highest educatio level by default. However, o ore tha the type of educatio syste is exogeous, is copulsory educatio exogeous. Oe therefore eeds to study costs ad beefits o the differet laguage groups of itroducig a copulsory educatio syste i order to assess its relevace. The odel does ot allow to distiguish betwee copulsory uiligual ad copulsory biligual systes. Uder each syste everybody lears to speak at least oe coo laguage, ish, perfectly, ad everybody attais a high skill level. Hece, the expected utility 22